1. Field of the Invention
The present invention relates to a position controlling device which is used for shaft control of a numerical control machine.
2. Description of the Related Art
Conventionally, controlling devices are used in which a driving system for accelerating and decelerating a structure to be driven is supported by and fixed to a base of the device, and displacement force acting on the base is compensated for by a reaction force of the structure to be driven. FIG. 11 is a model of a driving system schematically showing a mechanism of one shaft of the driving system in a machine tool, which is one type of machine which employs numerical control. The driving system has a structure in which a driving force Fx is imparted to a structure C to be driven by a servo motor (not shown) which moves on a structure B, which also functions as a guiding surface, in a direction x2. Structures A placed on both sides of the structure B support and fix the structure B, and one side of each structure A is rigidly mounted on and fixed to the ground. When the structure C to be driven is accelerated or decelerated in the x2 direction, the structure A which is the base receives the reaction force from the structure C to be driven, deforms in a direction x1, and generates vibration. On the structure B, a linear scale (not shown) for detecting the position x2 of the structure to be driven is provided.
Next, equations of motion are determined assuming the driving system model of FIG. 11 as a target plant. In this case, as the generalized coordinate system, the position x2 of the structure to be driven and the displacement x1 of the base may be used, and the following two equations of motion can be obtained:(Mb+Mc)·d2x1/dt2=Mc·d2x2/dt2+Ra·x1=0  (1)Mc{d2x2/dt2−d2x1/dt2}=Fx  (2)wherein Mb represents a mass Mb of the structure B, Mc represents a mass Mc of the structure C to be driven, and Ra represents a directional rigidity Ra of the structure A in the direction of x1.
FIG. 12 is a block diagram showing the equations of motion (1) and (2) for the target plant, and will be described in detail in the description of the preferred embodiments of the present invention to be described later.
FIG. 13 is a block diagram of a position controlling device of a related art. A position instruction value X which is generated by an upper device (not shown) employing a function is input to an acceleration and deceleration processor 50. For a position instruction value Xc output by the acceleration and deceleration processor 50, a second-order functional acceleration and deceleration process is applied in the acceleration and deceleration processor 50 so that the second order derivative with respect to time of dXc/dt is bounded even when the derivative of X with respect to time, dX/dt is step-shaped. In order to accelerate a position instruction response, the position instruction value Xc is differentiated with respect to time in differentiators 54 and 55 (S is a Laplacian operator), to calculate feed forward amounts Vf and Af of the instruction velocity and the instruction acceleration. A conversion block Cb is a conversion block for determining a feed forward amount of thrust which corresponds to the motor thrust for generating the acceleration Af, and is usually substituted by multiplying the mass Mc of the structure C to be driven to the acceleration Af.
As the position detection value of the target plant 58, the position x2 of the structure to be driven, which is detected by the above-described linear scale is used. The position x2 of the structure to be driven is subtracted from the position instruction value Xc by a subtractor 51, and a position deviation output by the subtractor 51 is amplified by a factor of Gp by a position deviation amplifier Gp, and the velocity feed forward amount Vf is added to the output of the position deviation amplifier Gp in an adder 52, to obtain a velocity instruction value V. A subtractor 53 subtracts, from the velocity instruction value V, a velocity v of the structure to be driven which is obtained by differentiating the position x2 of the structure to be driven with respect to time by a differentiator 56, and the output of the subtractor 53 which is a velocity deviation is amplified by a velocity deviation amplifier Gv. The velocity deviation amplifier Gv generally comprises a proportional integration amplifier and various filters for inhibiting high-frequency vibration phenomena generated in the order of hundred Hz of the target plant. The output of the velocity deviation amplifier Gv and the velocity feed forward amount Vf are added by an adder 57, and an output of the adder becomes the motor generated thrust, that is, the driving force Fx of the structure C to be driven.
FIG. 14 shows a result of a simulation of a second-order functional acceleration response (maximum acceleration 2 [m/sec2]) of the position controlling device of the related art of FIG. 13, when the target plant parameters are set to Mb=500 [Kg], Mc=300 [Kg], and Ra=19.6·106 [Nm/m], and the amplifications Gp and Gv which are control parameters are preferably adjusted. The position controlling device 200 in this case attempts to control the absolute position (x2−x1) of the structure to be driven of the target plant according to the position instruction value Xc, as shown in FIG. 11. However, because the position controlling device 200 of FIG. 13 does not consider the displacement x1 of the base, a large error in absolute position εo=Xc−(x2−x1) is caused during acceleration as shown in FIG. 14.
FIG. 15 is a block diagram showing another example structure of a position controlling device of a related art. This device has a structure in which a compensation block for the displacement of base x1 shown in JP 2007-025961 A is added. A structure of the added portion will now be described.
A base vibration monitor correspondent block 59 of FIG. 15 is a block corresponding to a base vibration monitor of JP2007-025961 A. Because there is no dumping component in the base vibration, the operation of this block according to JP 2007-025961 A which is Xsw=McS2/(MbS2+Ra)Xc becomes a unstable transfer function, and, thus, Xsw=(McS2/Ra)Xc is employed in the exemplified structure, placing more importance on the operation under constant acceleration. Here, Xsw represents an instruction value for base vibration compensation. An adder 60 adds the position instruction value Xc to the base vibration compensation instruction value Xsw, resulting in a position instruction value Xco for control. The base vibration compensation instruction value Xsw is also differentiated with respect to time by differentiators 61 and 63 so that a velocity instruction value Vsw for base vibration compensation and an acceleration instruction value Asw for base vibration compensation are calculated. The velocity instruction value Vsw is added to the velocity feed forward amount Vf in an adder 62, and the acceleration instruction value Asw is multiplied by the mass Mc of the structure to be driven and results in a thrust instruction value Fsw for base vibration compensation, which is in turn added with thrust feed forward amount Ff in an adder 64.
FIG. 16 shows a result of a simulation of a response when target plant parameters, control parameters, and a second-order functional acceleration process similar to FIG. 14 are applied on the position controlling device of related art of FIG. 15. Because a control structure which compensates the base displacement is employed, the error εo of the absolute position is reduced. However, because there is no dumping component, the response has a remaining vibration at the start and end of acceleration generated by an acceleration derivative instruction value Bc (=d3Xc/dt3), with the vibration being enlarged as the instruction value Bc is increased.
FIG. 17 is a block diagram of another example structure of a position controlling device of related art. In this example structure, the technique described by Akihiro YAMAMOTO (and four others) in “High-Speed Positioning Control for Linear Motor Driving Table without Base Vibration”, Journal of the Japan Society for Precision Engineering, Supplement Contributed Papers, Japan Society for Precision Engineering, 2004, Vol. 70, No. 5, p. 645-650 is used. The thrust feed forward is realized using an inverse transfer function of the target plant and the vibration of the base is inhibited. Next, portions which differ from the position controlling devices of the related art which are already described will be described.
A transfer function P2 indicates a transfer function from the driving force Fx to the position x2 of the structure to be driven, and is given by the following Equation 3 based on FIG. 12.P2={(Mb+Mc)S2+Ra}/{McS2(MbS2+Ra)}  (3)Here, because the inverse transfer function P2−1 of the transfer function P2 is not stable, a transfer function F represented by the following Equation 4 is considered in order to set P2−1·F which has a stable pole (S=−ωo) of a first-order delay component.F={ωo/(S+·ωo)}{(Mb+Mc)S2+Ra}/Ra  (4)Thus, P2−1·F is:P2−1·F={ωoMcS2(MbS2+Ra)}/{(S+ωo)Ra}  (5)A feed forward amount Ff of thrust is calculated with Ff=P2−1·F·Xc, and the thrust feed forward amount Ff in FIG. 11 can be calculated because a third-order derivative of the position instruction value Xc with respect time is bounded.
FIG. 18 shows a result of a simulation of a response when target plant parameters, control parameters, and a second-order functional acceleration process similar to FIG. 14 are applied to the position controlling device of related art of FIG. 17 with the parameter ωo=10000. Fundamentally, because a structure is employed in which the position x2 of the structure to driven matches the position instruction value Xco for control, inhibition of the vibration of the response is achieved. However, when velocity instruction value Vc is not zero (Vc≠0), an error in absolute position εo remains during shaft operation due to occurrence of a position instruction deviation εc=Xc−Xco.